What is necessary to do for private labelling?

Hi there,
I am close to making my first order for private label product (Yuhuuu!!). I have a question about that:

What is necessary to do for private labelling? Is it done just by using your UPC code and brand name on the listing or is it necessary to customize your product and boxing with you logo and brand name?

If customizing product and boxing is not mandatory, would you still recommend it for the first order? I was thinking of reducing expenses as much as possible to try the market out but I wonder if it´s that important to do the branding right away from the beginning.

Any insight on this will be very much appreciated.
Thanks and keep up with this helpful group!!